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So what I'm gathering here is that the "sport direct shift" is most likely a computer controlled process rather than a mechanical difference inside the transmission itself. Doesn't mean there's absolutely no difference, but that leaves me assuming it may require an ECM tune alongside the TCM swap to make that handshake go nicely.
I have no idea if it will work but even if it did the LS will still be a pretty slow car but it would shift hard up and down, for me it would be a "juice isn't worth the squeeze" mod that might have some drivability issues. I do have lots of respect for anyone trying to make this work though